Directions : Study the following information carefully to answer the given…
2022
Directions : Study the following information carefully to answer the given questions:
Two buses P and Q start their journey from bus depot to different destinations. Bus P starts 12km in south and reach at point 1. Then turns left and travel 13km to reach at point 2. Then turns right and travel 14km to reach at point 3. After that it turns left and travels 18km to reach at point 4. Then bus P turns to left and travel 9km to reach final stops 5. Bus Q travel 16km in east of depot to reach at point 6. Now turns right and travel 11km to reach at point 7. Then turns left and travel 22km to reach at point 8. Then turns left and travel 14km to reach at point 9. Finally turns left and travel 39km to reach at point 10.
These stops are assigned names according to the given below conditions:
* If the distance between two consecutive points is prime number, then first stops is called ‘A’
* If the stops (points) are in north-west and south-east of bus depot, then these points are called ‘B’
* If the stops (points) are in north-east of bus depot, then these points are called ‘C’
* If the distance between two consecutive points is even number, then first stops is called ‘D’
Ajay takes E-rikshaw from bus depot and goes 8km in west direction then takes left and goes 6km to reach his house. Find the shortest between Ajay’s house and stop 1?
- A.
12km
- B.
10km
- C.
Can’t be determined
- D.
14km
- E.
20km
Show answer & explanation
Correct answer: B
Concept
Direction-and-distance problems are solved on a coordinate grid: fix the depot at the origin, take east as +x and north as +y, and translate each leg into a coordinate change. A LEFT turn rotates the facing 90 degrees anticlockwise (N to W to S to E to N); a RIGHT turn rotates it 90 degrees clockwise (N to E to S to W to N). Once both endpoints have coordinates, the shortest straight-line distance is the Pythagorean distance d = sqrt of the sum of the squared coordinate differences.
Application - locate Stop 1
Bus P begins at the depot (0, 0) and goes 12 km south, so Stop 1 sits at (0, -12). Only Stop 1 is needed here, so the later legs of Bus P and all of Bus Q can be ignored for this question.
Application - locate Ajay's house
Ajay also starts at the depot (0, 0):
Go 8 km west: position = (-8, 0).
Facing west, a LEFT turn faces south; go 6 km south: house = (-8, -6).
Application - shortest distance
The horizontal gap between the house (-8, -6) and Stop 1 (0, -12) is |0 - (-8)| = 8 km; the vertical gap is |-12 - (-6)| = 6 km. These are the two legs of a right triangle:
d = sqrt(82 + 62)
d = sqrt(64 + 36) = sqrt(100)
d = 10 km
So the shortest distance between Ajay's house and Stop 1 is 10 km.
Cross-check
The legs 6, 8, 10 are the classic 3-4-5 right triangle scaled by 2, confirming the result is exactly 10 with no rounding. The 'Can't be determined' value is ruled out because every leg has a fixed length and direction, so both points are uniquely pinned on the grid.